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On complete intersections in varieties with finite-dimensional motive

Abstract : Let X be a complete intersection inside a variety M with finite-dimensional motive and for which the Lefschetz-type conjecture B (M) holds. We show how conditions on the niveau filtration on the homology of X influence directly the niveau on the level of Chow groups. This leads to a generalization of Voisin's result. The latter states that if M has trivial Chow groups and if X has non-trivial variable cohomology parametrized by c-dimensional algebraic cycles, then the cycle class maps A(k)(X) -> H-2k (X) are injective for k < c. We give variants involving group actions, which lead to several new examples with finite-dimensional Chow motives.
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Contributeur : Imb - Université de Bourgogne <>
Soumis le : vendredi 5 juillet 2019 - 12:15:56
Dernière modification le : mardi 10 novembre 2020 - 17:14:04

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Robert Laterveer, Jan Nagel, Chris Peters. On complete intersections in varieties with finite-dimensional motive. Quarterly Journal of Mathematics, Oxford University Press (OUP), 2019, 70 (1), pp.71-104. ⟨10.1093/qmath/hay038⟩. ⟨hal-02174842⟩



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